Results 1 
8 of
8
Rectangular tileability and complementary tileability are undecidable
"... Does a given set of polyominoes tile some rectangle? We show that this problem is undecidable. In a different direction, we also consider tiling a cofinite subset of the plane. The tileability is undecidable for many variants of this problem. However, we present an algorithm for testing whether th ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Does a given set of polyominoes tile some rectangle? We show that this problem is undecidable. In a different direction, we also consider tiling a cofinite subset of the plane. The tileability is undecidable for many variants of this problem. However, we present an algorithm for testing whether the complement of a finite region is tileable by a set of rectangles.
The complexity of generalized domino tilings
"... Abstract. Tiling planar regions with dominoes is a classical problem, where the decision and counting problems are polynomial. We prove a variety of hardness results (both NP and #Pcompleteness) for different generalizations of dominoes in three and higher dimensions. 1. ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. Tiling planar regions with dominoes is a classical problem, where the decision and counting problems are polynomial. We prove a variety of hardness results (both NP and #Pcompleteness) for different generalizations of dominoes in three and higher dimensions. 1.
Research Statement
"... My main research field is Macroeconomics. My research agenda takes the problem of broadly defined individual optimal choice as its central topical concern. Fascinated by the fact that uninsurable risk and heterogeneity can have substantial impact on aggregate economic outcomes, and on the impact of ..."
Abstract
 Add to MetaCart
(Show Context)
My main research field is Macroeconomics. My research agenda takes the problem of broadly defined individual optimal choice as its central topical concern. Fascinated by the fact that uninsurable risk and heterogeneity can have substantial impact on aggregate economic outcomes, and on the impact of government policies, I depart from the representative agent framework and explore the role of heterogeneity in macroeconomics. My research methodology is to set up a utilitymaximizing model of intertemporal individual choice. The process involves extensive and complex numerical calculation. Given the model, I then carry out numerical simulations, which show how a change in model’s parameters affects the outcome, and compare the implication of the model with empirical data. Using this approach, I have been conducting research on housing, consumption, wealth inequality, labor supply, and education. I now briefly describe my current research in those areas, carried out by myself alone and with separate coauthors. • Housing I have completed several papers based on my Ph. D. dissertation ([1], [2]). These papers set up an overlapping generations, generalequilibrium model of life cycle choices of
FAST DOMINO TILEABILITY
"... Abstract. Domino tileability is a classical problem in Discrete Geometry, famously solved by Thurston for simply connected regions in nearly linear time in the area. In this paper, we improve upon Thurston’s height function approach to a nearly linear time in the perimeter. 1. ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. Domino tileability is a classical problem in Discrete Geometry, famously solved by Thurston for simply connected regions in nearly linear time in the area. In this paper, we improve upon Thurston’s height function approach to a nearly linear time in the perimeter. 1.
COMPLEXITY OF COUNTING PLANAR TILINGS BY TWO BARS
"... Abstract. We show that the problem of determining the number of ways of tiling a planar figure with a horizontal and a vertical bar is #Pcomplete. We build off of the results of Beauquier, Nivat, Remila, and Robson in [1] in which they showed that the problem determining existence of such tilings w ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We show that the problem of determining the number of ways of tiling a planar figure with a horizontal and a vertical bar is #Pcomplete. We build off of the results of Beauquier, Nivat, Remila, and Robson in [1] in which they showed that the problem determining existence of such tilings was shown to be NPcomplete. 1.